given the pre - image abcd and the image after a dilation, abcd, what is true about the polygons? check all…

given the pre - image abcd and the image after a dilation, abcd, what is true about the polygons? check all that apply. the length ab is 2. the length ab is 3. the image is smaller than the pre - image. the scale factor is $\frac{3}{2}$. the scale factor is $\frac{2}{3}$.

given the pre - image abcd and the image after a dilation, abcd, what is true about the polygons? check all that apply. the length ab is 2. the length ab is 3. the image is smaller than the pre - image. the scale factor is $\frac{3}{2}$. the scale factor is $\frac{2}{3}$.

Answer

Explanation:

Step1: Calculate length of AB

Count the grid - units between A and B. AB has a length of 3 units. So the statement "The length AB is 2" is false.

Step2: Calculate length of A'B'

Count the grid - units between A' and B'. A'B' has a length of 2 units. So the statement "The length A'B' is 3" is false.

Step3: Compare size of pre - image and image

Since the length of A'B' (2 units) is less than the length of AB (3 units), the image is smaller than the pre - image. This statement is true.

Step4: Calculate scale factor

The scale factor $k=\frac{\text{length of corresponding side in image}}{\text{length of corresponding side in pre - image}}=\frac{A'B'}{AB}=\frac{2}{3}$. So the statement "The scale factor is $\frac{3}{2}$" is false and the statement "The scale factor is $\frac{2}{3}$" is true.

Answer:

  • The image is smaller than the pre - image.
  • The scale factor is $\frac{2}{3}$.